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BookCard:Gilbert Strang (1991), Calculus.
書誌情報 ;Title :Calculus ;Author :Gilbert Strang ;Publisher :Wellesley, Mass. : Wellesley-Cambridge Press, ©1991. ;Edition/Format :Book : English ;Document Type: Book / Internet Resource - Downloadable computer file ;All Authors / Contributors :Gilbert Strang ;Find more information about: ;ISBN :0961408820 9780961408824 ;OCLC Number :22510764(Book), 439739685(Internet Resource) ;Notes :Includes index. ;Description :xii, 614, 31, 7 p. : col. ill. ; 26 cm(Book). / Mode of access: World Wide Web.; System requirements: Adobe Acrobat Reader. ;Responsibility :Gilbert Strang. 目次 1. Introduction to Calculus 1. Velocity and Distance :速度と距離 translated byきったん氏 2. Calculus Without Limits :極限を使わない微積分学 translated byきったん氏 3. The Velocity at an Instant :瞬間速度 translated byきったん氏 4. Circular Motion :円運動 translated byきったん氏 5. A Review of Trigonometry :三角比の概論 translated byきったん氏 6. A Thousand Points of Light :千の光点 translated byきったん氏 7. Computing in Calculus 2. Derivatives 1. The Derivative of a Function 2. Powers and Polynomials 3. The Slope and the Tangent Line 4. Derivative of the Sine and Cosine 5. The Product and Quotient and Power Rules 6. Limits 7. Continuous Functions 3. Applications of the Derivative 1. Linear Approximation 2. Maximum and Minimum Problems 3. Second Derivatives: Minimum vs. Maximum 4. Graphs 5. Ellipses, Parabolas, and Hyperbolas 6. Iterations x_{n+1} = F(x_{n}) 7. Newton's Method and Chaos 8. The Mean Value Theorem and l'Hôpital's Rule 4. The Chain Rule 1. Derivatives by the Chain Rule 2. Implicit Differentiation and Related Rates 3. Inverse Functions and Their Derivatives 4. Inverses of Trigonometric Functions 5. Integrals 1. The Idea of the Integral 2. Antiderivatives 3. Summation vs. Integration 4. Indefinite Integrals and Substitutions 5. The Definite Integral 6. Properties of the Integral and the Average Value 7. The Fundamental Theorem and Its Consequences 8. Numerical Integration 6. Exponentials and Logarithms 1. An Overview 2. The Exponential ex 3. Growth and Decay in Science and Economics 4. Logarithms 5. Separable Equations Including the Logistic Equation 6. Powers Instead of Exponentials 7. Hyperbolic Functions 7. Techniques of Integration 1. Integration by Parts 2. Trigonometric Integrals 3. Trigonometric Substitutions 4. Partial Fractions 5. Improper Integrals 8. Applications of the Integral 1. Areas and Volumes by Slices 2. Length of a Plane Curve 3. Area of a Surface of Revolution 4. Probability and Calculus 5. Masses and Moments 6. Force, Work, and Energy 9. Polar Coordinates and Complex Numbers 1. Polar Coordinates 2. Polar Equations and Graphs 3. Slope, Length, and Area for Polar Curves 4. Complex Numbers 10. Infinite Series 1. The Geometric Series 2. Convergence Tests: Positive Series 3. Convergence Tests: All Series 4. The Taylor Series for ex, sin x, and cos x 5. Power Series 11. Vectors and Matrices 1. Vectors and Dot Products 2. Planes and Projections 3. Cross Products and Determinants 4. Matrices and Linear Equations 5. Linear Algebra in Three Dimensions 12. Motion along a Curve 1. The Position Vector 2. Plane Motion: Projectiles and Cycloids 3. Tangent Vector and Normal Vector 4. Polar Coordinates and Planetary Motion 13. Partial Derivatives 1. Surfaces and Level Curves 2. Partial Derivatives 3. Tangent Planes and Linear Approximations 4. Directional Derivatives and Gradients 5. The Chain Rule 6. Maxima, Minima, and Saddle Points 7. Constraints and Lagrange Multipliers 14. Multiple Integrals 1. Double Integrals 2. Changing to Better Coordinates 3. Triple Integrals 4. Cylindrical and Spherical Coordinates 15. Vector Calculus 1. Vector Fields 2. Line Integrals 3. Green's Theorem 4. Surface Integrals 5. The Divergence Theorem 6. Stokes' Theorem and the Curl of F 16. Mathematics after Calculus 1. Linear Algebra 2. Differential Equations 3. Discrete Mathematics 紹介 Book Description Gilbert Strang's Calculus textbook is ideal both as a course companion and for self study. The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. About the Author Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology and an Honorary Fellow of Balliol College, of the University of Oxford, UK. His current research interests include linear algebra, wavelets and filter banks, applied mathematics, and engineering mathematics. He is the author or co-author of six textbooks and has published a monograph with George Fix titled “An Analysis of the Finite Element Method.” Professor Strang served as SIAM’s president from 1999-2000, chaired the US National Committee on Mathematics from 2003–2004, and won the Neumann Medal of the US Association of Computational Mechanics in 2005. He is a fellow of the American Academy of Arts and Sciences. 便利な情報 Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide. * The complete textbook (PDF - 38.5MB) Textbook Components * Table of Contents (PDF) * Answers to Odd-Numbered Problems (PDF) * Equations (PDF) Category:ブックカード